Using Transition Systems to Formalize Ideas from Vedānta

Abstract

Abstract: Vedānta is one of the oldest philosophical systems. While there are many detailed commentaries on Vedānta, there are very few mathematical descriptions of the different concepts developed there. This article shows how ideas from theoretical computer science can be used to explain Vedānta. The standard ideas of transition systems and modal logic are used to develop a formal description for the different ideas in Vedānta. The generality of the formalism is illustrated via a number of examples including saṃsāra, Patañjali’s Yogasūtras, karma, the three avasthās from the Māṇḍūkya Upaniṣad and the key difference between advaita and dvaita in relation to mokṣa.